Corrected Principal Component Regression and Its Application in China's Urban Employment Demand

摘要

In this paper, we use the principal component regression to study the 16 influence factors of urban employment demand. In theory, we derive the mathematical models of corrected principal component regression. Ordinary principal component regression is the dependent variable doing multiple linear regression with the first several principal components, and corrected principal component regression is the dependent variable doing multiple linear regression with several principal components. In the empirical analysis, first of all, the ordinary multivariate linear regression does not pass the variable significance test, the reason is the multicollinearity between the independent variables. Stepwise regression and principal component regression both can eliminate the multicollinearity. For the data set in this paper, among the significant regressions, from the aspect of prediction within the sample, stepwise regression is the best, the principal component regression is more and more good with the increase of the number of principal components; From the aspect of prediction outside the sample, under the criterion of average minimum of the absolute value of the relative error in the prediction, the corrected principal component regression with the 1, 3, 4, 5, 6, and 8 principal components is one of the best in all kinds of regression methods. Finally, we obtain the optimal regression equation, and give some economic explanations of the model.